He thought, "If someone was going to reward me with the abstract knowledge that I’m able to motivate myself to do really hard things using only hypothetical rewards, would I be able to do it?” After that, he kept up his usual light-grocery-load pace all the way home, and made it there in 6 minutes.

Notice the wording of that. I'll modify it a bit to make my point.

If I do this, I will have justified belief that I can motivate myself to do really hard things using only hypothetical rewards, which itself counts as a hypothetical reward. I've seen people do amazing things via Löbian reasoning in the past, so I'm about 80% confident it'll work. Now I shall test this hypothesis.

Notice what he didn't say. He didn't say, "Am I the kind of person who can do this?" and then lie to himself in the hopes of becoming that kind of person. Nor did he say, "Do I want to be the kind of person who can do this?"

No part of you needs to believe false things--or even exaggerated truths--about personal identity to make stuff like this work when you have timeless decision theory. You can just believe true things about your brain and mammalian behavioral psychology and manipulate the world accordingly.